A family of sparse polynomial systems arising in chemical reaction systems
Journal of Symbolic Computation
Investigating Generic Methods to Solve Hopf Bifurcation Problems in Algebraic Biology
AB '08 Proceedings of the 3rd international conference on Algebraic Biology
Journal of Symbolic Computation
On proving the absence of oscillations in models of genetic circuits
AB'07 Proceedings of the 2nd international conference on Algebraic biology
CASC'10 Proceedings of the 12th international conference on Computer algebra in scientific computing
Chemical reaction systems, computer algebra and systems biology
CASC'11 Proceedings of the 13th international conference on Computer algebra in scientific computing
Semi-algebraic description of the equilibria of dynamical systems
CASC'11 Proceedings of the 13th international conference on Computer algebra in scientific computing
On Muldowney's criteria for polynomial vector fields with constraints
CASC'11 Proceedings of the 13th international conference on Computer algebra in scientific computing
Computing hopf bifurcations in chemical reaction networks using reaction coordinates
CASC'12 Proceedings of the 14th international conference on Computer Algebra in Scientific Computing
CASC'12 Proceedings of the 14th international conference on Computer Algebra in Scientific Computing
PoCaB: a software infrastructure to explore algebraic methods for bio-chemical reaction networks
CASC'12 Proceedings of the 14th international conference on Computer Algebra in Scientific Computing
Hi-index | 0.00 |
A family of polynomial differential systems describing the behavior of a chemical reaction network with generalized mass action kinetics is investigated. The coefficients and monomials are given by graphs. The aim of this investigation is to clarify the algebraic-discrete aspects of a Hopf bifurcation in these special differential equations. We apply concepts from toric geometry and convex geometry. As usual in stoichiometric network analysis we consider the solution set as a convex polyhedral cone and we intersect it with the deformed toric variety of the monomials. Using Grobner bases the polynomial entries of the Jacobian are expressed in different coordinate systems. Then the Hurwitz criterion is applied in order to determine parameter regions where a Hopf bifurcation occurs. Examples from chemistry illustrate the theoretical results.